Related papers: Binary contraction method for the construction of …
The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in…
This paper proposes a theory that bridges classical analytical mechanics and nonequilibrium thermodynamics. Its intent is to derive the evolution equations of a system from a stationarity principle for a suitably augmented Lagrangian…
We study the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non…
In previous papers we have introduced a natural nonequilibrium free energy by considering the functional describing the large fluctuations of stationary nonequilibrium states. While in equilibrium this functional is always convex, in…
In this Letter, three physical predictions on the phase separation of binary systems are derived based on a dynamic transition theory developed recently by the authors. First, the order of phase transitions is precisely determined by the…
We develop the geometrical, analytical, and computational framework for reactive island theory for three degrees-of-freedom time-independent Hamiltonian systems. In this setting, the dynamics occurs in a 5-dimensional energy surface in…
The lack of a mechanistic framework for chemical reactions forming inorganic extended solids presents a challenge to accelerated materials discovery. We demonstrate here a combined computational and experimental methodology to tackle this…
We propose a new approach to represent nonparametrically the linear dependence structure of a spatio-temporal process in terms of latent common factors. Though it is formally similar to the existing reduced rank approximation methods…
The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase transitions for binary systems using either the classical…
Individual components such as cells, particles, or agents within a larger system often require detailed understanding of their relative position to act accordingly, enabling the system as a whole to function in an organised and efficient…
This paper addresses the derivation of a two-phase flow model accounting for surface tension effects, by means of the Stationary Action Principle (SAP). The Lagrangian functional, defining the Action, is composed of a kinetic energy,…
The numerical solutions of nonlocal and local Boltzmann kinetic equations for the simulation of central heavy ion reactions are parameterized in terms of time dependent thermodynamical variables in the Fermi liquid sense. This allows one to…
The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…
In this paper we develop a hybrid version of the encounter-based approach to diffusion-mediated absorption at a reactive surface, which takes into account stochastic switching of a diffusing particle's conformational state. For simplicity,…
This paper proposes the first free-stream boundary condition in a purely Lagrangian framework for weakly-compressible smoothed particle hydrodynamics (WCSPH). The boundary condition is implemented based on several numerical techniques,…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
The usual formulations of time-dependent mechanics start from a given splitting $Y=R\times M$ of the coordinate bundle $Y\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a…
We consider solid state phase transformations that are caused by free energy densities with domains of non-convexity in strain-composition space; we refer to the non-convex domains as mechano-chemical spinodals. The non-convexity with…
Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state…
Dynamical transitions, such as a change from bound to unbound motion, often occur as post-adiabatic crossings of a time-dependent separatrix. Whether or not any given orbit will include such a crossing transition typically depends…